Question

|x+8|+|x+y-6|=0
Va implor ​

Answer 1

$\it |x+8|\geq0,\ \forall x\in\mathbb{R}\ \ \ \ \ \ \ \ \ (1)\\ \\ |x+y-6|\geq0,\ \forall x,\ y\in\mathbb{R}\ \ \ \ \ (2)\\ \\ |x+8|+|x+y-6|=0\ \ \ \ \ \ (3)\\ \\ (1),\ (2),\ (3)\ \Rightarrow\ \begin{cases}\it |x+8|=0 \Rightarrow x+8=0 \Rightarrow x=-8\ \ \ \ \ \ \ (4)\\ \\ \it |x+y-6|=0 \Rightarrow x+y-6=0\stackrel{(4)}{\Longrightarrow}-8+y-6=0 \Rightarrow y=14\end{cases}$